Question:
There are two children in a family. If it is known that at least one child is a boy, find the that both children are boys.
There are two children in a family. If it is known that at least one child is a boy, find the that both children are boys.
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Use conditional probability: \( P(A|B) = \frac{P(A \cap B)}{P(B)} \).
Updated On: Mar 3, 2025
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Solution and Explanation
Possible outcomes for two children (B = Boy, G = Girl):
\[
\{BB, BG, GB, GG\}
\]
Given that at least one child is a boy, the sample space reduces to:
\[
\{BB, BG, GB\}.
\]
The 64abecb1454319c1ac04f9e6 of both being boys:
\[
P(BB | \text{at least one boy}) = \frac{P(BB)}{P(BB, BG, GB)} = \frac{1}{3}.
\]
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